Cloud providers handle substantial number of requests to create and delete virtual machines (VMs) on a daily basis, where the unknown sequence of requests eventually leads to resource fragmentation. To mitigate this issue, periodic consolidation of VMs into fewer number of physical hosts is an important cost-saving procedure, closely related to the vector bin-packing problem. In this paper, we propose the BalCon algorithm for consolidation that steadily reduces the number of active hosts and keeps migration costs low. BalCon classifies the cluster's state and selects one of three heuristics to balance resources for superior consolidation. To evaluate BalCon's performance with respect to optimality, we introduce integer programming models. BalCon finds 99.7% of the optimal solutions for over 750 problem instances. This outstanding result was achieved due to the Force Step of our algorithm, which is the key improvement detail for common heuristics. We compare BalCon with a modified Sercon heuristic using Huawei and synthetic datasets with two resources for allocation.

翻译：云提供商每天处理大量创建和删除虚拟机的请求，这些未知序列的请求最终会导致资源碎片化。为解决这一问题，定期将虚拟机整合到更少的物理主机上是一项重要的成本节约措施，这与向量装箱问题密切相关。本文提出了一种用于整合的BalCon算法，该算法能稳步减少活跃主机数量并保持较低的迁移成本。BalCon对集群状态进行分类，并选择三种启发式策略之一来平衡资源以实现更优整合。为评估BalCon在最优性方面的性能，我们引入了整数规划模型。BalCon在超过750个问题实例中找到了99.7%的最优解。这一卓越成果得益于我们算法中的"强制步骤"，这是对常见启发式方法的关键改进细节。我们使用华为数据集和两种资源的合成数据集，将BalCon与改进的Sercon启发式算法进行了比较。